Sparse High-Dimensional Covariance Estimation via Pairwise Composite Likelihood

Alessandro CASA

Associate Professor - Free University of Bozen-Bolzano

Estimating covariance matrices in high-dimensional settings poses significant computational and statistical challenges. Pairwise likelihood offers a practical alternative to the full likelihood by considering only bivariate marginal distributions. In this work, we introduce a novel approach for estimating sparse high-dimensional covariance matrices by maximizing a truncated pairwise likelihood function. Our method strategically selects only those pairwise likelihood terms corresponding to nonzero covariance elements, leading to significant computational gains and improved interpretability. The truncation is guided by minimizing the L2​-distance between pairwise and full likelihood scores, coupled with an L1​-penalty to promote sparsity at the level of pairwise likelihood components. Unlike traditional penalization methods that shrink individual covariance parameters, our technique performs direct selection of pairwise likelihood objects, thereby preserving the unbiasedness of the underlying estimating equations. We will present theoretical results establishing the selection consistency of our procedure, demonstrating its ability to correctly identify the nonzero covariance structure even as the dimensionality grows. Furthermore, we will showcase the empirical performance of our method on both synthetic and real-world datasets, highlighting its effectiveness in achieving stable and accurate covariance estimation.

In collaboration with Center for Applied Statistics in Business and Economics